Question

1. a 16 - centimeter rod is held between a flashlight and a wall as shown. find the length of the shadow on the wall if the rod is 25 cm from the wall and 20 cm from the light.

Explanation:

Step1: Set up proportion

We can set up a proportion using similar - triangles. Let the length of the shadow be $x$. The ratio of the distance from the light to the rod to the distance from the light to the wall is equal to the ratio of the length of the rod to the length of the shadow. The distance from the light to the rod is $20$ cm and the distance from the light to the wall is $20 + 25=45$ cm, and the length of the rod is $16$ cm. So, $\frac{20}{45}=\frac{16}{x}$.

Step2: Cross - multiply

Cross - multiplying the proportion $\frac{20}{45}=\frac{16}{x}$ gives us $20x = 16\times45$.

Step3: Solve for $x$

First, calculate $16\times45 = 720$. Then, we have $20x=720$. Divide both sides by $20$: $x=\frac{720}{20}=36$.

Answer:

$36$ cm